Details

Time bar (total: 10.4s)

sample179.0ms

Algorithm
intervals
Results
107.0ms133×body1280valid
27.0ms62×body640valid
11.0ms256×pre80true
6.0ms20×body320valid
3.0ms29×body80valid
2.0ms12×body160valid

simplify21.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0155
1225
2335
3395
4505
5705
6995
71245
81665
92595
102605
112605

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b
(+ x (- (tan (+ y z)) (tan a)))
0.2b
(- (tan (+ y z)) (tan a))
2.4b
(tan (+ y z))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
19×add-sqr-sqrt
18×prod-diff
17×add-cube-cbrt
11×associate-+r+
10×add-log-exp
4×tan-quot
3×pow1 add-exp-log expm1-log1p-u fma-def fma-neg add-cbrt-cube log1p-expm1-u
2×sub-neg tan-sum diff-log sum-log frac-sub distribute-lft-out distribute-lft-out--
1×+-commutative associate-+r- flip3-- flip3-+ flip-- flip-+ difference-of-squares
Counts
3 → 72
Calls
3 calls:
8.0ms
(+ x (- (tan (+ y z)) (tan a)))
8.0ms
(- (tan (+ y z)) (tan a))
3.0ms
(tan (+ y z))

series278.0ms

Counts
3 → 9
Calls
3 calls:
115.0ms
(+ x (- (tan (+ y z)) (tan a)))
110.0ms
(- (tan (+ y z)) (tan a))
53.0ms
(tan (+ y z))

simplify91.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0276685
1732540
23128507
35001488

prune224.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
0.1b
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.2b
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b
(* (tan y) (tan z))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
165×*-un-lft-identity
115×add-sqr-sqrt
108×add-cube-cbrt prod-diff
97×times-frac
56×associate-+r+
27×distribute-lft-out
18×fma-neg
16×associate-/r/
11×add-log-exp
9×flip3-- flip--
8×add-exp-log add-cbrt-cube div-inv
7×tan-quot
6×pow1
4×expm1-log1p-u log1p-expm1-u associate-/l*
3×fma-def associate-*r* associate-*l* associate-/r* associate-/l/
2×sub-neg flip3-+ diff-log sum-log flip-+ distribute-lft-out-- difference-of-squares
1×cbrt-undiv +-commutative frac-times associate-+r- frac-2neg associate-*r/ div-exp pow-prod-down associate-*l/ frac-add prod-exp clear-num *-commutative frac-sub cbrt-unprod unswap-sqr
Counts
4 → 227
Calls
4 calls:
12.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
76.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
46.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms
(* (tan y) (tan z))

series992.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
327.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
367.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
91.0ms
(* (tan y) (tan z))

simplify78.0ms

Algorithm
egg-herbie
Counts
239 → 239
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
07044504
122933782
250023674

prune691.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (tan a))
0.6b
(cbrt (tan a))
0.6b
(cbrt (tan a))
60.4b
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×tan-quot cbrt-div pow1/3
1×fma-udef
Counts
4 → 52
Calls
4 calls:
1.0ms
(cbrt (tan a))
1.0ms
(cbrt (tan a))
1.0ms
(cbrt (tan a))
0.0ms
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

series524.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(cbrt (tan a))
115.0ms
(cbrt (tan a))
118.0ms
(cbrt (tan a))
176.0ms
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

simplify102.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 4 (96.0ms)

IterNodesCost
0102427
1211373
2675363
32633349
45002337

prune371.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (tan a))
0.6b
(cbrt (tan a))
0.6b
(cbrt (tan a))
60.2b
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (log1p (expm1 (cbrt (tan a)))) (* (cbrt (tan a)) (cbrt (tan a)))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×tan-quot cbrt-div pow1/3
1×fma-udef
Counts
4 → 52
Calls
4 calls:
1.0ms
(cbrt (tan a))
1.0ms
(cbrt (tan a))
1.0ms
(cbrt (tan a))
0.0ms
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (log1p (expm1 (cbrt (tan a)))) (* (cbrt (tan a)) (cbrt (tan a)))))

series935.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(cbrt (tan a))
121.0ms
(cbrt (tan a))
118.0ms
(cbrt (tan a))
583.0ms
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (log1p (expm1 (cbrt (tan a)))) (* (cbrt (tan a)) (cbrt (tan a)))))

simplify79.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 4 (75.0ms)

IterNodesCost
091468
1184412
2495382
31846355
45003249

prune351.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes305.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02931
12931

end0.0ms

sample5.0s

Algorithm
intervals
Results
3.1s3957×body1280valid
895.0ms1985×body640valid
340.0ms8000×pre80true
201.0ms657×body320valid
106.0ms1113×body80valid
64.0ms288×body160valid